The 20-year-old midfield has been on loan with the Bulls for two months, making 11 appearances.
Head of Football Tim Harris says the player has great commitment and has a bright future in football.
"Kyle is someone we've known for a while and has shown a great commitment and desire to sign for ourselves and we are pleased that he has agreed to make the switch and join us on a permanent deal," Harris told the club's official website.
"He, like Tom Owen Evans and several others, have a bright future in the game and it's important that we look after these players as we ourselves look to progress.
"The whole squad is coming together and the work Marc and Will are doing on the training ground is showing that we are getting more and more competitive each week, as the recent results against Kidderminster, Chester and Chorley have proved.
"However, we are always looking to improve the squad and increase the competition for places as and when the right player becomes available."
Later Finn tweeted: Thanks to everyone @Coventry_City . Time to kick on with my career and get this great club @HerefordFC back to where it should be